A Model of Chaos

A Model of Chaos

It’s a familiar situation: A couple goes through a bitter breakup and their mutual friends have to choose sides. Sociologists have studied this type of situation, but in recent years, some researchers have looked at ways to model it mathematically.

That’s because such models could prove useful in many ways—from helping predict key players in a political or business conflict to refining the way online social networks display information.

In a paper published recently in the Proceedings of the National Academy of Sciences, researchers from Cornell University describe a model for predicting how a social group will break apart during a turbulent split. Jon Kleinberg, a professor of computer science at Cornell, who led the work, says researchers have traditionally focused on predicting how a group will look once the conflict has shaken out. He says this work proposes a way of looking at the process of the split itself.

Kleinberg notes that his group’s model doesn’t apply to every situation. Instead, it portrays extremely polarizing conflicts. A sociological theory called “structural balance” describes the decisions that group members are forced to make when a group splits completely apart. The model best fits ” situations where the logic starts to become, ‘If you’re not with me, you’re against me,’” Kleinberg says.

The researchers tested their model on data documenting the split of a university karate club, as well as to the division between the Axis and the Allies in World War II. They modeled the stages of the karate club’s split correctly, except for one error. For World War II, the model correctly predicted the side chosen by every country except Denmark and Portugal.

Kleinberg says the models have not been thoroughly tested on other situations, but it’s easy to watch a simulation and imagine the interpersonal relationships playing out. For example, in one model he ran, one side coalesced quickly, while the other group seemed to form only after each of its members was isolated from the first group.

Sidney Redner, a professor of physics at Boston University who has also worked on modeling how groups split apart, says the researchers’ work is very sophisticated, but there’s a long way to go before we have a clean understanding of the process. He adds that it’s notoriously hard to apply models like this to the real world. For example, he says, efforts to use theories like this to predict violence between Los Angeles street gangs have not been successful so far.